We investigate the dependence of Cluster high-latitude magnetopause and low-latitude flank flux transfer events (FTEs) on solar wind conditions using measurements from Cluster FGM and CIS and ACE MFI and SWEPAM between February 2001 and June 2003. We find that there are strong dependences of Cluster FTE occurrence on the IMF Bxgsm, Bygsm, and Bzgsm components but not on the IMF magnitude. There are strong dependences of Cluster FTE occurrence on the IMF clock, tilt, spiral, and cone angles. However, some patterns are significantly different from previous results. The solar wind density, speed, Beta, VxBz, dynamic pressure, and magnetosonic Mach number have different degrees of control on FTE occurrence. FTE separation time is found to be clearly controlled by IMF Bygsm, Bzgsm, and magnitude, and the IMF clock, tilt, spiral, and cone angles, and weakly controlled by the solar wind VxBz and magnetosonic Mach number. There is no obvious control of it by other IMF and solar wind parameters. FTE peak-peak magnitude is found to be controlled by IMF Bygsm, Bzgsm, and magnitude and by the solar wind density and dynamic pressure but not by other IMF and solar wind parameters. The FTE dawn-dusk asymmetry is not likely caused by the Parker spiral IMF. Some FTE statistical patterns are strongly dependent on FTE locations. Finally, we see ~4% of the FTEs corresponding to a single change in IMF Bzgsm from positive to negative, ~4% corresponding to a single change from negative to positive, and ~43% corresponding to multiple changes in the sign of IMF Bzgsm, all within the 10-min interval preceding the FTEs. There is still no evidence for a direct correlation between IMF Bzgsm changing sign and FTEs.